Convert Cycles Hair Particle System to Mesh Object
I had the same issue converting hair particle into mesh, then trying to bake it in a low-poly model to use in a game engine. I found that there's no one-click solution built into the Blender, so here's my work-around:


Convert the particle into edge loops (click "convert" button in the modifier stack)
Convert the edge loops into bezier curves (select the edge loops and hit AltC)
Make them solid and shape them up using bevel and taper objects (Properties Panel > Object Data > Geometry)
Finally convert them back into mesh object (select the object and AltC)


You need to do quite a few steps in this workflow but it yields more control over final shapes.